Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life

Robin Wilson

When I first received this book, I thought it had been damaged en route. The dust jacket had small tears in it and even some chunks missing. Taking a closer look, I quickly realized that the dust jacket was actually intact with no tears; it was simply designed to look worn, as if the book had been around since Charles Dodgson’s time. Inside, the pages looked like any other book although nearly half of them contained pictures or illustrations. Coupled with the book’s short length (a little over two hundred pages) and nontechnical nature (aimed at a general audience), this made for a quick read. A high percentage of the text is direct quotes from Dodgson via letters, books, and various publications, including some originally only intended for his siblings. The effect will be entertaining for those who enjoy Dodgson’s arithmetical and logical games. Indeed, the quotes are so numerous that it is almost as if Dodgson had written the book himself. Biographical details are provided for context, but the emphasis is clearly on Dodgson’s mathematics.

For this reviewer, the most interesting part concerned Dodgson’s “matrix cipher.” It is not what we think of today as matrix encryption (a.k.a. the Hill cipher, after Lester Hill), but rather a method of encipherment that begins with the alphabet arranged in a rectangular array (referred to as a matrix), like the Polybius and Playfair ciphers, and uses no linear algebra. This system had previously been analyzed in a Cryptologia article, “Matrix Cipher of C. L. Dodgson” by Stanley H. Lipson and Francine Abeles (Volume XIV Number 1 (January 1990) pp. 28-36).

The book succeeds in being understandable to a general audience. The task is made a bit simpler by the fact that Dodgson’s work was not on extremely difficult problems, so that there are no heavy prerequisites. The most advanced work reproduced is his well known “Method of Condensation” for finding determinants and the author does an excellent job in presenting the necessary background from scratch. This particular topic has also been presented elsewhere recently. See for example The College Mathematics Journal, “Shutting up like a telescope”: Lewis Carroll’s “Curious” Condensation Method for Evaluating Determinants by Adrian Rice and Eve Torrence, pp. 85-95, March 2007 (vol. 38 no.2) and, by the same authors, Math Horizons, “Lewis Carroll's Condensation Method of Evaluating Determinants,” Volume 14, Nov. 2006. The 2007 paper is incorrectly referenced in Wilson’s book as “College Mathematical Journal 38 (February 2007).” Although I wasn’t acting as a proofreader, this was the only error I noticed. The book seems to have been written with great care.

Other topics of interest include Dodgson’s work on voting schemes (none are fair in all cases), Venn diagrams, and his book Euclid and his Modern Rivals. I had heard of this book before and assumed it dealt with non-Euclidean geometry. It does not — it simply critiques recent texts that attempted to improve upon The Elements by presenting Euclidean geometry in a different manner. Dodgson rejected all such attempts.

In summary, Wilson’s latest effort will likely be enjoyed by everyone who is a fan of Lewis Carroll, be they mathematicians or not.